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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math.analysis.interpolation;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math.DuplicateSampleAbscissaException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math.analysis.polynomials.PolynomialFunctionLagrangeForm;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math.analysis.polynomials.PolynomialFunctionNewtonForm;<a name="line.23"></a>
<FONT color="green">024</FONT>    <a name="line.24"></a>
<FONT color="green">025</FONT>    /**<a name="line.25"></a>
<FONT color="green">026</FONT>     * Implements the &lt;a href="<a name="line.26"></a>
<FONT color="green">027</FONT>     * "http://mathworld.wolfram.com/NewtonsDividedDifferenceInterpolationFormula.html"&gt;<a name="line.27"></a>
<FONT color="green">028</FONT>     * Divided Difference Algorithm&lt;/a&gt; for interpolation of real univariate<a name="line.28"></a>
<FONT color="green">029</FONT>     * functions. For reference, see &lt;b&gt;Introduction to Numerical Analysis&lt;/b&gt;,<a name="line.29"></a>
<FONT color="green">030</FONT>     * ISBN 038795452X, chapter 2.<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * The actual code of Neville's evaluation is in PolynomialFunctionLagrangeForm,<a name="line.32"></a>
<FONT color="green">033</FONT>     * this class provides an easy-to-use interface to it.&lt;/p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     *<a name="line.34"></a>
<FONT color="green">035</FONT>     * @version $Revision: 825919 $ $Date: 2009-10-16 16:51:55 +0200 (ven. 16 oct. 2009) $<a name="line.35"></a>
<FONT color="green">036</FONT>     * @since 1.2<a name="line.36"></a>
<FONT color="green">037</FONT>     */<a name="line.37"></a>
<FONT color="green">038</FONT>    public class DividedDifferenceInterpolator implements UnivariateRealInterpolator,<a name="line.38"></a>
<FONT color="green">039</FONT>        Serializable {<a name="line.39"></a>
<FONT color="green">040</FONT>    <a name="line.40"></a>
<FONT color="green">041</FONT>        /** serializable version identifier */<a name="line.41"></a>
<FONT color="green">042</FONT>        private static final long serialVersionUID = 107049519551235069L;<a name="line.42"></a>
<FONT color="green">043</FONT>    <a name="line.43"></a>
<FONT color="green">044</FONT>        /**<a name="line.44"></a>
<FONT color="green">045</FONT>         * Computes an interpolating function for the data set.<a name="line.45"></a>
<FONT color="green">046</FONT>         *<a name="line.46"></a>
<FONT color="green">047</FONT>         * @param x the interpolating points array<a name="line.47"></a>
<FONT color="green">048</FONT>         * @param y the interpolating values array<a name="line.48"></a>
<FONT color="green">049</FONT>         * @return a function which interpolates the data set<a name="line.49"></a>
<FONT color="green">050</FONT>         * @throws DuplicateSampleAbscissaException if arguments are invalid<a name="line.50"></a>
<FONT color="green">051</FONT>         */<a name="line.51"></a>
<FONT color="green">052</FONT>        public PolynomialFunctionNewtonForm interpolate(double x[], double y[]) throws<a name="line.52"></a>
<FONT color="green">053</FONT>            DuplicateSampleAbscissaException {<a name="line.53"></a>
<FONT color="green">054</FONT>    <a name="line.54"></a>
<FONT color="green">055</FONT>            /**<a name="line.55"></a>
<FONT color="green">056</FONT>             * a[] and c[] are defined in the general formula of Newton form:<a name="line.56"></a>
<FONT color="green">057</FONT>             * p(x) = a[0] + a[1](x-c[0]) + a[2](x-c[0])(x-c[1]) + ... +<a name="line.57"></a>
<FONT color="green">058</FONT>             *        a[n](x-c[0])(x-c[1])...(x-c[n-1])<a name="line.58"></a>
<FONT color="green">059</FONT>             */<a name="line.59"></a>
<FONT color="green">060</FONT>            PolynomialFunctionLagrangeForm.verifyInterpolationArray(x, y);<a name="line.60"></a>
<FONT color="green">061</FONT>    <a name="line.61"></a>
<FONT color="green">062</FONT>            /**<a name="line.62"></a>
<FONT color="green">063</FONT>             * When used for interpolation, the Newton form formula becomes<a name="line.63"></a>
<FONT color="green">064</FONT>             * p(x) = f[x0] + f[x0,x1](x-x0) + f[x0,x1,x2](x-x0)(x-x1) + ... +<a name="line.64"></a>
<FONT color="green">065</FONT>             *        f[x0,x1,...,x[n-1]](x-x0)(x-x1)...(x-x[n-2])<a name="line.65"></a>
<FONT color="green">066</FONT>             * Therefore, a[k] = f[x0,x1,...,xk], c[k] = x[k].<a name="line.66"></a>
<FONT color="green">067</FONT>             * &lt;p&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>             * Note x[], y[], a[] have the same length but c[]'s size is one less.&lt;/p&gt;<a name="line.68"></a>
<FONT color="green">069</FONT>             */<a name="line.69"></a>
<FONT color="green">070</FONT>            final double[] c = new double[x.length-1];<a name="line.70"></a>
<FONT color="green">071</FONT>            System.arraycopy(x, 0, c, 0, c.length);<a name="line.71"></a>
<FONT color="green">072</FONT>    <a name="line.72"></a>
<FONT color="green">073</FONT>            final double[] a = computeDividedDifference(x, y);<a name="line.73"></a>
<FONT color="green">074</FONT>            return new PolynomialFunctionNewtonForm(a, c);<a name="line.74"></a>
<FONT color="green">075</FONT>    <a name="line.75"></a>
<FONT color="green">076</FONT>        }<a name="line.76"></a>
<FONT color="green">077</FONT>    <a name="line.77"></a>
<FONT color="green">078</FONT>        /**<a name="line.78"></a>
<FONT color="green">079</FONT>         * Returns a copy of the divided difference array.<a name="line.79"></a>
<FONT color="green">080</FONT>         * &lt;p&gt;<a name="line.80"></a>
<FONT color="green">081</FONT>         * The divided difference array is defined recursively by &lt;pre&gt;<a name="line.81"></a>
<FONT color="green">082</FONT>         * f[x0] = f(x0)<a name="line.82"></a>
<FONT color="green">083</FONT>         * f[x0,x1,...,xk] = (f(x1,...,xk) - f(x0,...,x[k-1])) / (xk - x0)<a name="line.83"></a>
<FONT color="green">084</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.84"></a>
<FONT color="green">085</FONT>         * &lt;p&gt;<a name="line.85"></a>
<FONT color="green">086</FONT>         * The computational complexity is O(N^2).&lt;/p&gt;<a name="line.86"></a>
<FONT color="green">087</FONT>         *<a name="line.87"></a>
<FONT color="green">088</FONT>         * @param x the interpolating points array<a name="line.88"></a>
<FONT color="green">089</FONT>         * @param y the interpolating values array<a name="line.89"></a>
<FONT color="green">090</FONT>         * @return a fresh copy of the divided difference array<a name="line.90"></a>
<FONT color="green">091</FONT>         * @throws DuplicateSampleAbscissaException if any abscissas coincide<a name="line.91"></a>
<FONT color="green">092</FONT>         */<a name="line.92"></a>
<FONT color="green">093</FONT>        protected static double[] computeDividedDifference(final double x[], final double y[])<a name="line.93"></a>
<FONT color="green">094</FONT>            throws DuplicateSampleAbscissaException {<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>            PolynomialFunctionLagrangeForm.verifyInterpolationArray(x, y);<a name="line.96"></a>
<FONT color="green">097</FONT>    <a name="line.97"></a>
<FONT color="green">098</FONT>            final double[] divdiff = y.clone(); // initialization<a name="line.98"></a>
<FONT color="green">099</FONT>    <a name="line.99"></a>
<FONT color="green">100</FONT>            final int n = x.length;<a name="line.100"></a>
<FONT color="green">101</FONT>            final double[] a = new double [n];<a name="line.101"></a>
<FONT color="green">102</FONT>            a[0] = divdiff[0];<a name="line.102"></a>
<FONT color="green">103</FONT>            for (int i = 1; i &lt; n; i++) {<a name="line.103"></a>
<FONT color="green">104</FONT>                for (int j = 0; j &lt; n-i; j++) {<a name="line.104"></a>
<FONT color="green">105</FONT>                    final double denominator = x[j+i] - x[j];<a name="line.105"></a>
<FONT color="green">106</FONT>                    if (denominator == 0.0) {<a name="line.106"></a>
<FONT color="green">107</FONT>                        // This happens only when two abscissas are identical.<a name="line.107"></a>
<FONT color="green">108</FONT>                        throw new DuplicateSampleAbscissaException(x[j], j, j+i);<a name="line.108"></a>
<FONT color="green">109</FONT>                    }<a name="line.109"></a>
<FONT color="green">110</FONT>                    divdiff[j] = (divdiff[j+1] - divdiff[j]) / denominator;<a name="line.110"></a>
<FONT color="green">111</FONT>                }<a name="line.111"></a>
<FONT color="green">112</FONT>                a[i] = divdiff[0];<a name="line.112"></a>
<FONT color="green">113</FONT>            }<a name="line.113"></a>
<FONT color="green">114</FONT>    <a name="line.114"></a>
<FONT color="green">115</FONT>            return a;<a name="line.115"></a>
<FONT color="green">116</FONT>        }<a name="line.116"></a>
<FONT color="green">117</FONT>    }<a name="line.117"></a>




























































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